Question: What's the first wrong statement in the proof below that $ \triangle CEB \cong \triangle CAB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{BC} \cong \overline{BD}$ $, \ $ $ \angle ABC \cong \angle DBE$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ $ \angle ACB \cong \angle ECF$ $, \ $ $ \overline{BC} \cong \overline{CF}$ $, \ $ and $\ $ $ \angle ABC \cong \angle CFE$ Proof $ \triangle DEB \cong \triangle CAB$ because AAS $ \angle CFE \cong \angle BEC$ because vertical angles are equal $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \angle CEF \cong \angle BCE$ because alternate interior angles are equal $ \triangle CAB \cong \triangle CEF$ because ASA $ \triangle CEB \cong \triangle CAB$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle BEC \cong \angle CFE$ is the first wrong statement.